import sympy as sym

x=sym.Symbol('x')
f1=sym.sin(x)/x
print(sym.limit(f1,x,0))
f2=(1+x)**(1/x)
print(sym.limit(f2,x,0))
print(sym.limit(f2,x,sym.oo))
f3=(1+1/x)**x
print(sym.limit(f3,x,0))
print(sym.limit(f3,x,sym.oo))

f1=x**2+2*x+1
print(sym.diff(f1,x))
print(sym.diff(f1,x,2))
f2=sym.sin(x)
print(sym.diff(f2,x))
y=sym.Symbol('y')
f3=x**2+2*x+y**3
print(sym.diff(f3,x))
print(sym.diff(f3,y))

f=2*x
print(sym.integrate(f,(x,0,1)))
t=sym.symbols('t')
f=2*t
g=sym.integrate(f,(t,0,x))
print(sym.integrate(g,(x,0,3)))
f=sym.E**x+2*x
print(sym.integrate(f,x))
